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arXiv · 1304.2323

Determinacy and Jónsson cardinals in $L(\mathbb{R})$

Steve Jackson·Richard Ketchersid·Farmer Schlutzenberg·W. Hugh Woodin
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Abstract

Assume $\mathsf{ZF}+\mathsf{AD}+V=L(\mathbb{R})$ and let $κ<Θ$ be an uncountable cardinal. We show that $κ$ is Jónsson, and that if $\mathrm{cof}(κ)=ω$ then $κ$ is Rowbottom. We also establish some other partition properties.

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Steve Jackson, Richard Ketchersid, Farmer Schlutzenberg, W. Hugh Woodin. 2015-11-02. Determinacy and Jónsson cardinals in $L(\mathbb{R})$. https://doi.org/10.1017/jsl.2014.49

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